Russia is willing to help Ukraine investigate the murder of Russian journalist Arkady Babchenko, a senior MP has said.

The call came after Mr Babchenko, who was scathingly critical of the Kremlin, was gunned down in the Ukrainian capital, Kiev, on Tuesday.

The 41-year-old had fled Russia last year, fearing for his life, and settled in Ukraine. He had served in the Russian army during the two wars in Chechnya in 1990s and became one of Russia’s best-known war reporters.

The multi-storey building where Russian opposition journalist Arkady Babchenko lived in Kiev (AP)

Vyacheslav Volodin, the speaker of the State Duma, told Russian news agencies that Russia would be happy to help with the investigation if Ukrainian authorities requested it.

Ukrainian authorities have said they think Mr Babchenko was killed because of his work.

Several Ukrainian politicians blamed the Kremlin for the killing – comments which Kremlin spokesman Dmitry Peskov dismissed as cynical.